We investigate language generation in the limit - a model by Kleinberg and Mullainathan [2024, NeurIPS] and extended by Li, Raman, and Tewari [2025]. While Kleinberg and Mullainathan proved generation is possible for all countable collections, [Li et al., 2025] defined a hierarchy of generation notions (uniform, non-uniform, and generatable) and explored their feasibility for uncountable collections. Our first set of results resolve two open questions of [Li et al., 2025] by proving finite unions of generatable or non-uniformly generatable classes need not be generatable. These follow from a stronger result: there is a non-uniformly generatable class and a uniformly generatable class whose union is non-generatable. This adds to the aspects along which language generation in the limit is different from traditional tasks in statistical learning theory like classification, which are closed under finite unions. In particular, it implies that given two generators for different collections, one cannot combine them to obtain a single "more powerful" generator, prohibiting this notion of boosting. Our construction also addresses a third of [Li et al., 2025]'s open questions on whether there are uncountable classes that are non-uniformly generatable and do not satisfy the eventually unbounded closure (EUC) condition introduced by Li, Raman, and Tewari. Our approach utilizes carefully constructed classes along with a novel diagonalization argument that could be of independent interest in the growing area of language generation.

We investigate language generation in the limit - a model by Kleinberg and Mullainathan and extended by Li, Raman, and Tewari. While Kleinberg and Mullainathan proved generation is possible for all countable collections, Li, Raman, and Tewari defined a hierarchy of generation notions (uniform, non-uniform, and generatable) and explored their feasibility for uncountable collections. Our first set of results resolve two open questions of Li et al. by proving finite unions of generatable or non-uniformly generatable classes need not be generatable. These follow from a stronger result: there is non-uniformly generatable class and a uniformly generatable class whose union is non-generatable. This adds to the aspects along which language generation in the limit is different from traditional tasks in statistical learning theory like classification, which are closed under finite unions. In particular, it implies that given two generators for different collections, one cannot combine them to obtain a single more powerful generator, prohibiting this notion of boosting. Our construction also addresses a third of Li et al.'s open questions on whether there are uncountable classes that are non-uniformly generatable and do not satisfy the eventually unbounded closure (EUC) condition introduced by Li et al. Our approach utilizes carefully constructed classes along with a novel diagonalization argument that could be of independent interest in the growing area of language generation.

We study language generation in the limit under bounded memory. In this task, a learner observes examples from an unknown target language one at a time and must eventually output only new valid examples. Prior work assumes access to the entire history, a strong assumption since realistic algorithms retain limited past information. Classical work in learning theory shows memory constraints dramatically alter learnability; we extend this to language generation. First, we study memoryless generators. Under a mild enumeration restriction, every countable collection of infinite languages remains generable without memory. Without this restriction, we exactly characterize when memoryless generation is possible. For finite collections, we characterize the optimal minimax density achievable by memoryless generators -- the best density guaranteed against any collection of a given size. This combinatorial bound relies on Sperner's theorem and symmetric chain decompositions. We further show that a sliding window of the last $W$ examples does not improve this worst-case density, whereas allowing it to store $b$ adaptively chosen past examples improves the achievable density for every $b \geq 1$. Finally, we revisit identification in the limit, where the learner must converge to a single correct hypothesis for the target language. We focus on its incremental variant, where the learner remembers only its previous guess. Here, although exact identification fails on a collection of just three languages, a mild relaxation requiring convergence to an ``approximate'' version of the target is achievable for every finite collection. These results show bounded memory affects these tasks differently: generation remains achievable for every countable collection, while density and identification are confined to finite collections, with guarantees weakening as the collection grows.

We initiate the study of language generation in the limit, a model recently introduced by Kleinberg and Mullainathan [KM24], under the constraint of differential privacy. We consider the continual release model, where a generator must eventually output a stream of valid strings while protecting the privacy of the entire input sequence. Our first main result is that for countable collections of languages, privacy comes at no qualitative cost: we provide an $\varepsilon$-differentially-private algorithm that generates in the limit from any countable collection. This stands in contrast to many learning settings where privacy renders learnability impossible. However, privacy does impose a quantitative cost: there are finite collections of size $k$ for which uniform private generation requires $Ω(k/\varepsilon)$ samples, whereas just one sample suffices non-privately. We then turn to the harder problem of language identification in the limit. Here, we show that privacy creates fundamental barriers. We prove that no $\varepsilon$-DP algorithm can identify a collection containing two languages with an infinite intersection and a finite set difference, a condition far stronger than the classical non-private characterization of identification. Next, we turn to the stochastic setting where the sample strings are sampled i.i.d. from a distribution (instead of being generated by an adversary). Here, we show that private identification is possible if and only if the collection is identifiable in the adversarial model. Together, our results establish new dimensions along which generation and identification differ and, for identification, a separation between adversarial and stochastic settings induced by privacy constraints.

Answers to these questions must begin by formalizing the specification for what a generative algorithm for language should be doing.

Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have presented diffusion as an alternative to existing pretrained language models. We view diffusion and existing language models as complementary. We demonstrate that encoder-decoder language models can be utilized to efficiently learn high-quality language autoencoders. We then demonstrate that continuous diffusion models can be learned in the latent space of the language autoencoder, enabling us to sample continuous latent representations that can be decoded into natural language with the pretrained decoder.

This paper introduces the retrieval-augmented framework for automatic fashion caption and hashtag generation, combining multi-garment detection, attribute reasoning, and Large Language Model (LLM) prompting. The system aims to produce visually grounded, descriptive, and stylistically interesting text for fashion imagery, overcoming the limitations of end-to-end captioners that have problems with attribute fidelity and domain generalization. The pipeline combines a YOLO-based detector for multi-garment localization, k-means clustering for dominant color extraction, and a CLIP-FAISS retrieval module for fabric and gender attribute inference based on a structured product index. These attributes, together with retrieved style examples, create a factual evidence pack that is used to guide an LLM to generate human-like captions and contextually rich hashtags. A fine-tuned BLIP model is used as a supervised baseline model for comparison. Experimental results show that the YOLO detector is able to obtain a mean Average Precision (mAP@0.5) of 0.71 for nine categories of garments. The RAG-LLM pipeline generates expressive attribute-aligned captions and achieves mean attribute coverage of 0.80 with full coverage at the 50% threshold in hashtag generation, whereas BLIP gives higher lexical overlap and lower generalization. The retrieval-augmented approach exhibits better factual grounding, less hallucination, and great potential for scalable deployment in various clothing domains. These results demonstrate the use of retrieval-augmented generation as an effective and interpretable paradigm for automated and visually grounded fashion content generation.

Generative adversarial networks (GANs) have great successes on synthesizing data. However, the existing GANs restrict the discriminator to be a binary classifier, and thus limit their learning capacity for tasks that need to synthesize output with rich structures such as natural language descriptions. In this paper, we propose a novel generative adversarial network, RankGAN, for generating high-quality language descriptions. Rather than training the discriminator to learn and assign absolute binary predicate for individual data sample, the proposed RankGAN is able to analyze and rank a collection of human-written and machine-written sentences by giving a reference group. By viewing a set of data samples collectively and evaluating their quality through relative ranking scores, the discriminator is able to make better assessment which in turn helps to learn a better generator. The proposed RankGAN is optimized through the policy gradient technique. Experimental results on multiple public datasets clearly demonstrate the effectiveness of the proposed approach.

Although quantum computing has been increasingly applied to replace classical computation, most existing quantum or hybrid models remain confined to simple tasks, with no successful application to large-scale natural language generation to date. In this work, we present the first hybrid quantum-classical large language model (LLM) for natural language generation, HyQuT, capable of performing coherent and context-aware dialogue. The proposed architecture integrates variational quantum circuits (VQCs) into the Transformer framework at both 8M and 150M parameter scales. Experimental results show that a minimal number of qubits (10 qubits with 80 quantum gates) can replace about 10% of the classical parameters in the 150M-parameter model, while achieving comparable convergence stability and generation quality. This study provides an early demonstration of the feasibility of integrating quantum computing to large-scale generative language models.